R Notebook

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Set the base directory for your analysis

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library(BSFG)

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The following code generates simulated data, and then loads it into the R workspace

can be skipped if you are loading your own data in a different way

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seed = 1  # for reproducibility
nSire = 50 # simulation design is a half-sib design: each of nSire fathers has nRep children, each with a different female
nRep = 10
nTraits = 4
nFixedEffects = 2 # fixed effects are effects on the factors
nFactors = 4
factor_h2s = c(rep(0,nFactors/2),rep(0.9,nFactors/2))  # factor_h2 is the % of variance in each factor trait that is explained by additive genetic variation.
# The is after accounting for the fixed effects on the factors
Va = 2 # residual genetic variance in each of the observed traits after accounting for the factors
Ve = 2 # residual microenvironmental variance in each of the observed traits after accounting for the factors
Vb = 0 # magnitude of the fixed effects (just factors)
new_halfSib_simulation('Sim_FE_1', nSire=nSire,nRep=nRep,p=nTraits, b=nFixedEffects, factor_h2s= factor_h2s,Va = Va, Ve = Ve,Vb = Vb)
set.seed(seed)
load('setup.RData')

Y = setup$Y
data = setup$data
K = setup$K
# Y[1:(nrow(Y)*3/4),1:(ncol(Y)/4)] = NA
# Y[(nrow(Y)/4)+1:(nrow(Y)/4),(ncol(Y)/4)+1:(ncol(Y)/4)] = NA
# Y[2*(nrow(Y)/4)+1:(nrow(Y)/4),2*(ncol(Y)/4)+1:(ncol(Y)/4)] = NA
# Y[3*(nrow(Y)/4)+1:(nrow(Y)/4),3*(ncol(Y)/4)+1:(ncol(Y)/4)] = NA

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Set the parameters of the BSFG model

see ?BSFG_control

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run_parameters = BSFG_control(
  max_NA_groups = 3,
  scale_Y = FALSE,   # should the columns of Y be re-scaled to have mean=0 and sd=1?
  simulation = TRUE, # Are you running against simulated data (ex from a call to new_halfSib_simulation above)? If so, you can provide the setup list and it will make some QC plots
  h2_divisions = 20, # Each variance component is allowed to explain between 0% and 100% of the total variation. How many segments should the range [0,100) be divided into for each random effect?
  h2_step_size = NULL, # if NULL, all possible values of random effects are tried each iteration. If in (0,1), a new candidate set of random effect proportional variances is drawn uniformily with a range of this size
  burn = 00,  # number of burn in samples before saving posterior samples
  K = 4 # number of factors
)

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Set the prior hyperparameters of the BSFG model

see ?BSFG_control

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priors = BSFG_priors(
  tot_Y_var = list(V = 0.5,   nu = 5),      # Prior variance of trait residuals after accounting for fixed effects and factors
  tot_F_var = list(V = 18/20, nu = 20),     # Prior variance of factor traits. This is included to improve MCMC mixing, but can be turned off by setting nu very large
  Lambda_prior = list(
    sampler = sample_Lambda_prec_horseshoe,
    prop_0 = 0.1,
    delta_l = list(shape = 3, rate = 1),
    delta_iterations_factor = 100
  ),
  B2_prior = list(
    sampler = sample_B2_prec_horseshoe,
    prop_0 = 0.1
  ),
  cis_effects_prior = list(
    prec = 1
  ),
  h2_priors_resids_fun = function(h2s,n)  1,  # Function that returns the prior density for any value of the h2s vector (ie the vector of random effect proportional variances across all random effects. 1 means constant prior. Alternative: pmax(pmin(ddirichlet(c(h2s,1-sum(h2s)),rep(2,length(h2s)+1)),10),1e-10),
  h2_priors_factors_fun = function(h2s,n) 1 # See above. Another choice is one that gives 50% weight to h2==0: ifelse(h2s == 0,n,n/(n-1))
)

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Construct the model

see ?BSFG_init

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options(error=recover)
BSFG_state = setup_model_BSFG(Y,            # n x p data matrix
                              ~(1|animal),  # RHS of base model for factors and residuals. Fixed effects defined here only apply to the factor residuals.
                              extra_regressions = list(X = model.matrix(~Fixed1,data)[,-1,drop=FALSE],factors=T,resids=F), # design matrix for additional fixed effects. These coefficients will be regularized with the B2_prior above. The same model can be used for both factors and resids
                              data,         # the data.frame with information for constructing the model matrices
                              relmat = list(animal = K), # covariance matrices for the random effects. If not provided, assume uncorrelated
                              run_parameters=run_parameters,
                              setup = setup, # only if running simulated data. Stores simulated values for comparison
                              run_ID = 'BSFG_example'
                                )

'BSFG_example' already exists

maps = make_Missing_data_map(BSFG_state)

  map N_groups max_group_size total_kept_NAs
1   1        1            500              0

BSFG_state = set_Missing_data_map(BSFG_state,maps$Missing_data_map)
BSFG_state = set_priors_BSFG(BSFG_state,priors)
BSFG_state = initialize_variables_BSFG(BSFG_state)

[1] "initializing Lambda_prec regularized horseshoe"
[1] "initializing B_prec regularized horseshoe"

BSFG_state = initialize_BSFG(BSFG_state)

[1] "Pre-calculating random effect inverse matrices for 1 groups of traits and 20 sets of random effect weights"

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BSFG_state = clear_Posterior(BSFG_state)

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Run MCMC

see ?sample_BSFG

A MCMC chain is a way of fitting parameters from a Bayesian model

The chain is a sequence of draws from the Posterior distribution of each parameter.

BSFG uses a Gibbs sampler, which means that we iterate through all of the model’s parameters

and for each parameter draw a new value from it’s posterior holding all other parameters constant

This works, but the individual draws are not independent draws from the joint posterior of all parameters.

Therefore, to get independent draws, we have to collect many posterior samples, and then save only a portion of them.

Also, it may take many iterations for the MCMC chain to converge to the central part of the distribution.

This is the burnin period, and we do not store these values (they are not useful).

At the end, we have a collection of samples from the posterior distribution of each parameter.

We can use these samples to characterize each distribution: mean, SD, histogram, HPDinterval, etc.

The way BSFG works is that you ask the program to collect a small number of samples

And then can assess how the chain is performing (how well it is mixing, is it converged?)

And then either save the samples as posterior samples, or declare them as burn-in and discard them.

Then, you can ask for more samples, and repeat until you have enough.

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Tools for re-setting Posterior samples, and helping chain converge

BSFG_state = clear_Posterior(BSFG_state)

BSFG_state = reorder_factors(BSFG_state)

n_samples = 200;  # how many samples to collect at once?
for(i  in 1:70) {
  print(sprintf('Run %d',i))
  BSFG_state = sample_BSFG(BSFG_state,n_samples,grainSize=1)  # run MCMC chain n_samples iterations. grainSize is a paramter for parallelization (smaller = more parallelization)
  
  BSFG_state = save_posterior_chunk(BSFG_state)  # save any accumulated posterior samples in the database to release memory
  print(BSFG_state) # print status of current chain
  plot(BSFG_state) # make some diagnostic plots. These are saved in a pdf booklet: diagnostic_plots.pdf
  # set of commands to run during burn-in period to help chain converge
  if(BSFG_state$current_state$nrun < BSFG_state$run_parameters$burn || i < 10) {
    BSFG_state = reorder_factors(BSFG_state,drop_cor_threshold = 0.6) # Factor order doesn't "mix" well in the MCMC. We can help it by manually re-ordering from biggest to smallest
    BSFG_state = clear_Posterior(BSFG_state)
    print(BSFG_state$run_parameters$burn)
  }
}

[1] "Run 1"

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Time difference of 1.117178 secs

 Current iteration: 200, Posterior_samples: 100 
 Current factor dimension: 4 factors 
 Total time: 1.117178 secs 

the standard deviation is zerono non-missing arguments to min; returning Infno non-missing arguments to max; returning -Inf

[1] 200
[1] "Run 2"

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Time difference of 1.218998 secs

 Current iteration: 400, Posterior_samples: 100 
 Current factor dimension: 4 factors 
 Total time: 2.336176 secs 

[1] 400
[1] "Run 3"

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Time difference of 1.258151 secs

 Current iteration: 600, Posterior_samples: 100 
 Current factor dimension: 4 factors 
 Total time: 3.594327 secs 

[1] 600
[1] "Run 4"

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Time difference of 1.235289 secs

 Current iteration: 800, Posterior_samples: 100 
 Current factor dimension: 4 factors 
 Total time: 4.829616 secs 

[1] 800
[1] "Run 5"

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Time difference of 1.190181 secs

 Current iteration: 1000, Posterior_samples: 100 
 Current factor dimension: 4 factors 
 Total time: 6.019797 secs 

[1] 1000
[1] "Run 6"

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Time difference of 1.315236 secs

 Current iteration: 1200, Posterior_samples: 100 
 Current factor dimension: 4 factors 
 Total time: 7.335033 secs 

[1] 1200
[1] "Run 7"

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Time difference of 1.235098 secs

 Current iteration: 1400, Posterior_samples: 100 
 Current factor dimension: 4 factors 
 Total time: 8.570131 secs 

[1] 1400
[1] "Run 8"

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Time difference of 1.132964 secs

 Current iteration: 1600, Posterior_samples: 100 
 Current factor dimension: 4 factors 
 Total time: 9.703095 secs 

[1] 1600
[1] "Run 9"

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Time difference of 1.156688 secs

 Current iteration: 1800, Posterior_samples: 100 
 Current factor dimension: 4 factors 
 Total time: 10.85978 secs 

[1] 1800
[1] "Run 10"

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Time difference of 1.258406 secs

 Current iteration: 2000, Posterior_samples: 100 
 Current factor dimension: 4 factors 
 Total time: 12.11819 secs 

[1] "Run 11"

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Time difference of 1.139323 secs

 Current iteration: 2200, Posterior_samples: 200 
 Current factor dimension: 4 factors 
 Total time: 13.25751 secs 

[1] "Run 12"

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Time difference of 1.223867 secs

 Current iteration: 2400, Posterior_samples: 300 
 Current factor dimension: 4 factors 
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[1] "Run 13"

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Time difference of 1.185764 secs

 Current iteration: 2600, Posterior_samples: 400 
 Current factor dimension: 4 factors 
 Total time: 15.66714 secs 

[1] "Run 14"

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Time difference of 1.206255 secs

 Current iteration: 2800, Posterior_samples: 500 
 Current factor dimension: 4 factors 
 Total time: 16.8734 secs 

[1] "Run 15"

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Time difference of 1.19526 secs

 Current iteration: 3000, Posterior_samples: 600 
 Current factor dimension: 4 factors 
 Total time: 18.06866 secs 

[1] "Run 16"

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Time difference of 1.27383 secs

 Current iteration: 3200, Posterior_samples: 700 
 Current factor dimension: 4 factors 
 Total time: 19.34249 secs 

[1] "Run 17"

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Time difference of 1.21709 secs

 Current iteration: 3400, Posterior_samples: 800 
 Current factor dimension: 4 factors 
 Total time: 20.55958 secs 

[1] "Run 18"

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Time difference of 1.173541 secs

 Current iteration: 3600, Posterior_samples: 900 
 Current factor dimension: 4 factors 
 Total time: 21.73312 secs 

[1] "Run 19"

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Time difference of 1.185308 secs

 Current iteration: 3800, Posterior_samples: 1000 
 Current factor dimension: 4 factors 
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[1] "Run 20"

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Time difference of 1.295601 secs

 Current iteration: 4000, Posterior_samples: 1100 
 Current factor dimension: 4 factors 
 Total time: 24.21403 secs 

[1] "Run 21"

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Time difference of 1.40123 secs

 Current iteration: 4200, Posterior_samples: 1200 
 Current factor dimension: 4 factors 
 Total time: 25.61526 secs 

[1] "Run 22"

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Time difference of 1.256207 secs

 Current iteration: 4400, Posterior_samples: 1300 
 Current factor dimension: 4 factors 
 Total time: 26.87146 secs 

[1] "Run 23"

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Time difference of 1.187128 secs

 Current iteration: 4600, Posterior_samples: 1400 
 Current factor dimension: 4 factors 
 Total time: 28.05859 secs 

[1] "Run 24"

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Time difference of 1.270541 secs

 Current iteration: 4800, Posterior_samples: 1500 
 Current factor dimension: 4 factors 
 Total time: 29.32913 secs 

[1] "Run 25"

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Time difference of 1.514377 secs

 Current iteration: 5000, Posterior_samples: 1600 
 Current factor dimension: 4 factors 
 Total time: 30.84351 secs 

[1] "Run 26"

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Time difference of 1.258334 secs

 Current iteration: 5200, Posterior_samples: 1700 
 Current factor dimension: 4 factors 
 Total time: 32.10185 secs 

———————————————————-

Work with the Posterior samples

———————————————————-

# reload the whole database of posterior samples
BSFG_state$Posterior = reload_Posterior(BSFG_state)
# all parameter names in Posterior
BSFG_state$Posterior$posteriorSample_params

 [1] "Lambda"       "U_F"          "F"            "delta"        "tot_F_prec"   "F_h2"         "tot_Eta_prec" "resid_h2"     "B1"           "B2_F"         "B2_R"         "U_R"         
[13] "cis_effects"  "Lambda_m_eff" "Eta"         

BSFG_state$Posterior$posteriorMean_params  # these ones only have the posterior mean saved, not individual posterior samples

[1] "Eta_mean"

# instead, load only a specific parameter
Lambda = load_posterior_param(BSFG_state,'Lambda')
# boxplots are good ways to visualize Posterior distributions on sets of related parameters
boxplot(BSFG_state$Posterior$F_h2[,1,])

# get posterior distribution on a function of parameters
# This is how to calculate the G-matrix for random effect #1 (ie animal above.)
G_samples = get_posterior_FUN(BSFG_state,Lambda %*% diag(F_h2['animal',]) %*% t(Lambda) + diag(resid_h2['animal',]/tot_Eta_prec[1,]))
# get posterior mean of a parameter
G = get_posterior_mean(G_samples)
# get Highest Posterior Density intervals for paramters
F_h2_HPD = get_posterior_HPDinterval(BSFG_state,F_h2)
boxplot(BSFG_state$Posterior$B1[,1,],outline=F);abline(h=0)

boxplot(BSFG_state$Posterior$B2_F[,1,],outline=F);abline(h=0)